Nonparametric Tests
BPS chapter 26
© 2006 W.H. Freeman and Company
Outliers
True or false: Outliers should always be removed from your dataset
since they interfere with Normality.
a)
b)
True
False
Outliers (answer)
True or false: Outliers should always be removed from your dataset
since they interfere with Normality.
a)
b)
True
False
Rank tests
Which rank test should you use if you have one sample of quantitative
data which is not Normally distributed but the population has a
continuous distribution?
a)
b)
c)
Wilcoxon rank sum test
Wilcoxon signed rank test
Kruskal-Wallis test
Rank tests (answer)
Which rank test should you use if you have one sample of quantitative
data which is not Normally distributed but the population has a
continuous distribution?
a)
b)
c)
Wilcoxon rank sum test
Wilcoxon signed rank test
Kruskal-Wallis test
Rank tests
Which rank test should you use if you have the differences for matched
pairs quantitative data which are not Normally distributed but the
population has a continuous distribution?
a)
b)
c)
Wilcoxon rank sum test
Wilcoxon signed rank test
Kruskal-Wallis test
Rank tests (answer)
Which rank test should you use if you have the differences for matched
pairs quantitative data which are not Normally distributed but the
population has a continuous distribution?
a)
b)
c)
Wilcoxon rank sum test
Wilcoxon signed rank test
Kruskal-Wallis test
Rank tests
Which rank test should you use if you have quantitative data for two
independent samples which are not Normally distributed but the
populations have continuous distributions?
a)
b)
c)
Wilcoxon rank sum test
Wilcoxon signed rank test
Kruskal-Wallis test
Rank tests (answer)
Which rank test should you use if you have quantitative data for two
independent samples which are not Normally distributed but the
populations have continuous distributions?
a)
b)
c)
Wilcoxon rank sum test
Wilcoxon signed rank test
Kruskal-Wallis test
Rank tests
Which rank test should you use if you have quantitative data for more
than two independent samples which are not Normally distributed
but the populations have continuous distributions?
a)
b)
c)
Wilcoxon rank sum test
Wilcoxon signed rank test
Kruskal-Wallis test
Rank tests (answer)
Which rank test should you use if you have quantitative data for more
than two independent samples which are not Normally distributed
but the populations have continuous distributions?
a)
b)
c)
Wilcoxon rank sum test
Wilcoxon signed rank test
Kruskal-Wallis test
Normal approximation
When do the Wilcoxon rank statistics become approximately Normal?
a)
b)
c)
d)
When the sample size(s) is/are small.
When the sample size(s) is/are large.
Always.
Never.
Normal approximation (answer)
When do the Wilcoxon rank statistics become approximately Normal?
a)
b)
c)
d)
When the sample size(s) is/are small.
When the sample size(s) is/are large.
Always.
Never.
Continuity correction
Why do we need to apply the continuity correction to the Wilcoxon rank
test statistics when we use the Normal approximation?
a)
b)
c)
d)
Because the sample size is small.
Because the sample size is large.
Because we are switching from a whole number only (discrete)
distribution to a continuous distribution.
Because we are switching from a continuous distribution to a whole
number only (discrete) distribution.
Continuity correction (answer)
Why do we need to apply the continuity correction to the Wilcoxon rank
test statistics when we use the Normal approximation?
a)
b)
c)
d)
Because the sample size is small.
Because the sample size is large.
Because we are switching from a whole number only (discrete)
distribution to a continuous distribution.
Because we are switching from a continuous distribution to a whole
number only (discrete) distribution.
Wilcoxon rank sum test
What additional condition must be met for this set of hypotheses to be
used?
H 0 : median1  median 2
H a : median1  median 2
Instead of these:
H 0 : The two distributions are the same.
H a : One has values that are systematically larger.
a)
b)
c)
d)
The distributions must be Normal.
The sample sizes must be large.
The distributions must have the same shape (but that shape doesn’t
have to be Normal).
The distributions must be continuous.
Wilcoxon rank sum test (answer)
What additional condition must be met for this set of hypotheses to be
used?
H 0 : median1  median 2
H a : median1  median 2
Instead of these:
H 0 : The two distributions are the same.
H a : One has values that are systematically larger.
a)
b)
c)
d)
The distributions must be Normal.
The sample sizes must be large.
The distributions must have the same shape (but that shape
doesn’t have to be Normal).
The distributions must be continuous.
Ties in rank tests
What happens if two data points are the same in a rank test?
a)
b)
c)
d)
Drop the two tied data points.
Number them like any other data points.
Assign each of the tied data points the average of the two rankings.
Move them to the end of the list.
Ties in rank tests (answer)
What happens if two data points are the same in a rank test?
a)
b)
c)
d)
Drop the two tied data points.
Number them like any other data points.
Assign each of the tied data points the average of the two
rankings.
Move them to the end of the list.
Ties within pairs for signed rank tests
What happens if an individual has the same before and after value in a
matched pairs setup for a signed rank test?
a)
b)
c)
d)
The resulting difference will be 0, so that difference is dropped from
the rankings.
Number them like any other data points.
Assign each of the tied data points the average of the two rankings.
Move them to the end of the list.
Ties within pairs for signed rank tests (answer)
What happens if an individual has the same before and after value in a
matched pairs setup for a signed rank test?
a)
b)
c)
d)
The resulting difference will be 0, so that difference is dropped
from the rankings.
Number them like any other data points.
Assign each of the tied data points the average of the two rankings.
Move them to the end of the list.